The function cosh(x), or hyperbolic cosine, is a mathematical function defined as the average of the exponential function e^x and its inverse e^(-x). It is expressed as cosh(x) = (e^x + e^(-x)) / 2. This function is commonly used in various fields, including physics and engineering, to model phenomena such as waveforms and structures. The graph of cosh(x) is a smooth, U-shaped curve that opens upwards, with its minimum value at cosh(0) = 1. Unlike the regular cosine function, cosh(x) does not oscillate; instead, it increases as x moves away from zero in both the positive and negative directions.